Lesson 1: Patterns and Numbers in Nature and the World

Patterns in Nature

the regularities that we see in the forms of the things in the natural world

Symmetry

if an imaginary line is drawn across an object, the resulting parts are mirrors of each other

Spiral

curved pattern that focuses on a center point and a series of circular shapes that revolve around it. This is common in plants and some
animals

Meander

is a series of regular sinuous curves, bends, loops, turns, or windings in the channel of a river, stream, or other watercourses. It is produced by a stream or river swinging from side to side as it flows across its floodplain or shifts its channel within a valley

Cracks

linear openings that form in materials to relieve stress. The pattern of cracks indicates whether the material is elastic or not

Stripe

a strip or band that has a different color from the surface surrounding it. This may be seen in various living things, especially animals

Logic reasoning and pattern observing

the first two math standards, which are the most important measurement of IQ and the core component of many careers

Logical patterns

usually the first to be observed since making categories or classification comes before numeration

aptitude tests

logic tests can be seen on ______ wherein takers are shown a sequence of pictures and asked to select which figure comes next among several choices

Relative Positional Rule

This is how the black square is positioned
inside each box

Movement Rule

This pertains to how the square moves in each box, in the clockwise direction

Geometric pattern

consists of shapes like polygons and circles that are repeated to create a design

Tessellation

a pattern that is formed by repeating polygons to cover a plane so that there are no gaps or overlaps

Regular tessellation

where a regular polygon is repeated

Semi-regular tessellation

with two or more regular polygons being repeated

Fractal

a never-ending pattern. It can be formed by continuously repeating something

Sierpinski Triangle

a fractal that is named after the Polish mathematician Waclaw Franciszek Sierpinski

Pascal's triangle

contains the numerical coefficients of binomial
expansions

Fractal Tree

To construct a ______, start at some point and draw a line segment. From an endpoint, draw two branches at a certain angle. Repeat the previous step to the new endpoints and continue the process to make more branches

Koch Snowflake

In drawing a _________, one needs to start by drawing an equilateral
triangle. Then, divide each side into three equal parts. After that, draw an equilateral
triangle on each middle part

Word Patterns

can be found in giving the plural of nouns, in forming the past tense of verbs, and in word analogy. They can also be found in the meters of poetry and in the rhythm of the words

Analogy

compares two different things, showing the relationship between them. The colons stand for words; single colon reads as “is to”, double colon reads “as”

Rhyme Scheme

the rhymes' pattern at the line of a poem or song (often in nursery rhymes)

Haiku

a Japanese poem, typically about nature, with 17 syllables divided into three lines of 5, 7, and 5 syllables

Number pattern

a list of numbers that follow a particular sequence or order

Arithmetic Sequence

an ordered set of numbers that have a common difference between each consecutive term

common difference

the difference between two consecutive terms

Geometric Sequence

goes from one term to the next by always multiplying or dividing by the same value

common ratio

a term is multiplied by a constant

Triangular numbers

The terms of a triangular sequence are related to the number of dots needed to create a triangle
1, 3, 6, 10, 15...

Square Numbers

the terms are the squares of their
position in the sequence
1, 4, 9, 16, 25

Cube Numbers

the terms are the cubes of their position
in the sequence
1, 8, 27, 64, 125